Continuum theory and phase-field simulation of magnetoelectric effects in multiferroic bismuth ferrite

Multiferroic materials possess electric and magnetic orderings simultaneously, making it possible to manipulate the electric state of a multiferroic by magnetic field, or vice versa. Among all single-phase multiferroics, BiFeO3 is particularly exciting, for its room temperature multiferroicity, excellent ferroelectric properties, and recently demonstrated electric control of antiferromagnetic domains, which opens door for its applications in spintronics. In this paper, we report a systematic theoretical and computational study on the structure and evolution of magnetoelectric domains in multiferroic BiFeO3. A continuum description is developed for antiferromagnetic ordering first, which is then incorporated into an unconventional phase field method that couples ferroelastic, ferroelectric, and antiferromagnetic orderings through the characteristic function of variants. The internal elastic, electric, and magnetic fields are carefully analyzed, taking into account both bulk and thin film geometries and boundary conditions. The theory is implemented into numerical simulations, where we not only observe the coupled ferroelectric and antiferromagnetic domains, and demonstrate the electric control of antiferromagnetic ordering, but also reveal the switching of antiferromagnetic domains by mechanical stress that is yet to be reported in experiment. Our study offers deep insight into the microstructural evolution and macroscopic properties of BiFeO3, and provides a powerful tool to study a wide range of multiferroic materials with magnetoelectric coupling.